Analytical model of atmospheric pressure, helium/trace gas radio-frequency capacitive Penning discharges

作者：Lieberman M A^*

来源：Plasma Sources Science and Technology, 2015, 24(2): 025009.

DOI：10.1088/0963-0252/24/2/025009

• atmospheric pressure discharge model
• Penning discharge model
• helium discharge model

Atmospheric and near-atmospheric pressure, helium/trace gas radio-frequency capacitive discharges have wide applications. An analytic equilibrium solution is developed based on a homogeneous, current-driven discharge model that includes sheath and electron multiplication effects and contains two electron populations. A simplified chemistry is used with four unknown densities: hot electrons, warm electrons, positive ions and metastables. The dominant electron-ion pair production is Penning ionization, and the dominant ion losses are to the walls. The equilibrium particle balances are used to determine a single ionization balance equation for the warm electron temperature, which is solved, both approximately within the alpha- and gamma-modes, and exactly by conventional root-finding techniques. All other discharge parameters are found, the extinction and alpha-gamma transitions are determined, and a similarity law is given, in which the equilibrium for a short gap at high pressure can be rescaled to a longer gap at lower pressure. Within the alpha-mode, we find the scaling of the discharge parameters with current density, frequency, gas density and gap width. The analytic results are compared to hybrid and particle-in-cell (PIC) results for He/0.1%N-2, and to hybrid results for He/0.1%H2O. For nitrogen, a full reaction set is used for the hybrid calculations and a simplified reaction set for the PIC simulations. For the chemically complex water trace gas, a set of 209 reactions among 43 species is used. The analytic results are found to be in reasonably good agreement with the more elaborate hybrid and PIC calculations.

• 出版日期2015-4